High spatial resolution diffraction and imaging using synchrotron X-rays are combined to monitor the incremental growth of a fatigue crack through the matrix of a Ti-6Al-4V/SCS-6 SiC monofilament metal matrix composite. X-ray tomography is used to quantify the crack opening displacement (COD) and diffraction to measure the crack-tip stress field in each phase, the wear degraded interfacial strengths, as well as the crack face tractions applied by the bridging fibres, at maximum () and minimum () loading as a function of crack length. In this way, it has been possible to quantify the crack-tip driving force (the stress intensity range effective at the crack-tip) in three ways: from the COD, the bridging stresses and the crack-tip stress field. The fibre stresses act to prop open the crack at and shield the crack at such that the change in COD is small over the fatigue cycle. Consequently, the effective stress intensity range at the crack tip remains around 10 MPa√m as the crack lengthens, as more and more fibres bridge the crack despite the normally applied stress intensity rising to 60 MPa√m. The implications of the derived fracture mechanics parameters are assessed and the wider potential of X-ray diffraction and imaging for crack-tip microscopy is discussed.
It has long been acknowledged that provided the fibres bridge the crack rather than fracture, excellent fatigue crack growth performance can be achieved for a long fibre metal matrix system such as a Ti-6Al-4V/SCS-6 SiC monofilament composite (Cotterill & Bowen 1993; Barney et al. 1998). This combined with excellent specific stiffness, elevated temperature strength and creep performance make such systems attractive for integrally bladed rings (Blings) and other aeroengine components (Hooker & Doorbar 2000; Ward-Close et al. 2001; Withers 2010). In view of the need for the crack to by-pass the fibres rather than fracture them, the interfacial strength between matrix and fibres is a key design parameter because this determines the degree of stress localization in the vicinity of the crack and the transfer of load to the fibres. For tests undertaken at low stress intensity factors, increasing fibre/matrix interfacial strength reduces the crack opening displacement (COD), causing crack arrest to occur earlier (fewer bridging fibres are required in the wake), presumably due to better transfer of stress to the fibres. However, increasing the interfacial strength increases the propensity for fibre fracture in the wake so that, the crack arrest/catastrophic failure transition occurs at lower stress intensities (Kaya & Bowen 2008).
The interfacial strengths and bridging stresses developed during fatigue crack growth have been a topic for considerable speculation (see figure 1). John and co-workers used COD measurements made at the surface to infer both crack-tip shielding (Kshield) and the distribution of bridging stresses over the crack faces for Timetal/SCS-6 SiC composites (Buchanan et al. 1997; John et al. 1998). By comparison with finite element simulations, Buchanan et al. (1997) inferred a bridging stress distribution similar to curve B in figure 1, with the average stress approximately 300 MPa (equivalent to an average bridging fibre stress of 900 MPa) and the fibre stress at the notch tip constant (approx. 1200 MPa) irrespective of crack length. Further they achieved excellent agreement with measured COD values and fatigue crack growth rates for a variety of test cases using a shear-lag model based on a constant interfacial strength of 9 MPa (John et al. 1998). This value is significantly lower than those measured by synchrotron diffraction for pristine SCS-6 fibres (see below). Consequently, direct experimental validation of both the distribution and magnitude of bridging stresses and its effect on the crack-tip driving force are required. Recent developments in X-ray tomography have opened the way for imaging of the fatigue crack at micron resolution. This stimulated early work looking at crack opening in long fibre composites at a relatively low resolution (Breunig et al. 1993). The higher resolution achievable at third generation synchrotron sources has opened the way for a number of quantitative studies of the COD, e.g. (Toda et al. 2003) and allows one to measure the COD profile across the whole crack front (Withers et al. 2006), rather than just at the free surfaces (Buchanan et al. 1997; Kaya & Bowen 2008). Furthermore, because X-ray tomography is a non-invasive method it is possible to monitor the progress of the crack in three dimensions as a function of fatigue crack growth (Withers et al. 2006).
Until recently, measurements of the interfacial strength of pristine fibre/matrix systems have been restricted to indirect measurements via modelling of push-out (Zeng et al. 2002), transverse tensioned push-out (Kalton et al. 1997) and full-fragmentation (Matikas 2007a,b, 2008) testing. In order to make direct measurements, we developed a modified version of the single fibre full-fragmentation test in which the fragmentation process is examined by synchrotron X-ray diffraction in situ prior to full-fragmentation (Preuss et al. 2002). Using this method, it has been shown that the frictional sliding stress of the interface for Ti-6Al-4V/SCS-6 SiC is dependent on the thermal-stress-related radial clamping force and so decreases from around 150 MPa at room temperature (RT) to 50 MPa at 400°C (Withers et al. 2010). More recently, we have used synchrotron diffraction to measure the distribution of interfacial strength along bridging fibres in the wake and ahead of a fatigue crack in individual fibres (Sinclair et al. 2005) or plies (Hung et al. 2009). This has shown that during fatigue cycling the frictional sliding strength for fibres in the vicinity of a fatigue crack falls dramatically to around 60 MPa at RT and 30 MPa at 300°C due to sliding wear (Hung & Withers 2012). This method also makes it possible to measure the stresses in the bridging fibres directly and thus to calculate their contribution to crack-tip shielding directly for the first time.
Here, we have combined the X-ray diffraction and imaging modes to form a crack-tip microscope analogous to an electron microscope (Withers 2011). Used together, they enable us to study the micromechanics and crack driving force for an advancing crack, to quantify key fracture mechanics parameters, and to compare the observations on real cracks with idealized models of fibre bridging and crack growth. This is the subject of this paper.
2. Experimental methods
(a) Fatigue testing
A unidirectional SiC/Ti-6Al-4V composite sample containing 35 vol% of 140 μm SCS-6 C-cored SiC fibres arranged approximately hexagonally was fabricated as described in Withers et al. (2006). Samples measuring approximately 100×4×1.4 mm3 were prepared for preliminary fatigue testing, which was carried out under three-point bending (3PB) using an Instron servo-hydraulic testing machine at the University of Birmingham. A notch was introduced using electrical discharge machining (EDM) to act as a crack initiator. An applied load ratio, R, of 0.1 was employed (ΔKApp=18.2 MPa√m), and the frequency was 5 Hz. After initial fatigue crack growth (Fs0), a smaller ‘dog-bone’ test-piece having a cross-section 2.48×1.08 mm2 (length (x)×width (y)) was excised by EDM having dimensions suitable for high-resolution X-ray tomography.
High-frequency fatigue cycling was undertaken off-line using a 2 kN BOSE mechanical fatigue test rig under tension–tension (T–T). The crack was grown in seven steps (Fs1–Fs7) until it was approximately half the length, W, of the sample (1200 μm). In order to prevent crack arrest, the stress nominal stress intensity (ΔKApp) had to be increased with increasing crack length, meaning that the load range (ΔP) decreased only slightly during the test. The crack growth parameters are summarized in table 1 and it is worth noting that the applied ΔKApp lies about 5 MPa√m above the applied threshold stress intensity as a function of crack length determined by Akinawa et al. (2007).
(b) Beamline configuration
On beamline ID15 at the ESRF, it is possible to switch quickly between the white beam mode used for fast-tomography (Di Michiel et al. 2005) and the monochromatic mode used for strain mapping (figure 2). The first monochromator acts as a ‘beam splitter’ reflecting the part of the white X-ray beam that satisfies Bragg's law. The second monochromator acts like a mirror, bringing the monochromatic beam parallel to the white beam. Both monochromators are used in the Laue geometry. The test-piece and the tensile rig (kindly provided by Buffiere and Maire at INSA, Lyon) were mounted on a translation stage in order to shift the sample between the positions required for the imaging and strain measurement experiments.
(c) Tomographic imaging
Nine hundred projections were acquired for each tomograph over a rotation range of 180°. An additional 51 images were acquired and used in determining the centre of rotation, dark and flat fields, and filtering, etc. Using region of interest tomography as described in Kyrieleis et al. (2009), only the volume containing the first 10 rows (out of 19) of fibres from the notch was included in the tomographs. These were recorded at the highest available spatial resolution (pixel size 1.59 μm) using an imaging detector comprising a LuAG:Ce scintillator, which converts X-ray absorption image into visible light, coupled to a 10×microscope optics and a Dalstar1M60 CCD camera (0.1 s per image). The image to detector distance was such that some phase contrast was obtained in addition to the attenuation contrast.
In order to calculate the COD, the reconstructed tomographic volumes were analysed using the VGStudio Max software. After increasing the contrast (figure 3a), a region-growing algorithm was used to select the cracked region. In this way, a binary volume was produced where the crack is characterized by intensity 0. In each column of pixels along the direction of the fibres (z-direction), the COD at that (x,y) position was calculated (using Matlab) from the number of pixels having intensity zero. In this way, a map of the COD was produced. Line profiles have been extracted from the COD map by taking the values along x at a fixed position y and then applying a Gaussian filter with size and standard deviation of 10 pixels.
(d) Strain mapping
The elastic matrix and fibre strains parallel to the loading axis (z) were subsequently measured by diffraction for the (102)Ti and (108)SiC peaks, respectively, using a procedure developed previously (Sinclair et al. 2004, 2005). The 100(x)×40(z) μm incident beam was oriented edge-on to the crack front. By repeatedly scanning vertically (z) and translating the sample by 120 μm in x each time it was possible to completely map the matrix and SiC elastic strains local to the crack-tip in two dimensions (x,z). The vertical (z) measurement spacing was finer (approx. 30 μm) closer to the crack plane than further from it (approx. 200 μm). The beam energy was set at 56 keV. Because the fibres were only loosely arranged in an hexagonal array (see figure 5); in practice, each z-scan does not correspond precisely to a unique ‘ply’. The unstressed lattice spacing d0 was determined for the matrix using a value representative of the crack flanks, which were assumed to be free of stress and varied little with applied loading. Because the fibres bridge the crack, it is probable that the fibres will not be stress-free near the crack. Consequently, the (far-field) thermal stresses were balanced at Fs0 by appropriate choice of d0 for the fibres. This d0 value was then applied to all fibres in all load steps.
(e) Experimental sequence
The following steps were undertaken at the ESRF:
Once the sample was mounted on the beam line, the load was applied statically.
The cracked region was tomographed.
The strain field was mapped in the vicinity of the fatigue crack by diffraction.
The load was then reduced to and steps 2–3 repeated.
The sample was removed and subjected to the next fatigue cycling increment before repeating steps 1–4.
(a) Evolution of crack morphology
Representative views illustrating the growth and morphology of the crack are shown in figure 4. It is clear that as the crack by-passes a fibre, the two halves of the crack front do not always reconnect immediately on the other side, as noted previously (Hung et al. 2009). As a result, a number of bifurcations can be seen with the crack front being non-planar and uneven.
A key fracture mechanics measure of the driving force for crack growth is provided by the COD. This has been measured directly from the three-dimensional tomographs as described in §2c and is plotted in figure 5. Only the damaged fibres on the exposed surfaces show any evidence of cracking (non-zero COD). It is clear that while the crack front is relatively uniform in length across the thickness in the early stages of growth (till Fs5), in the later stages crack advance is more pronounced on one side than on the other.
In common with previous observations (Withers et al. 2006), figure 5 shows that the COD is not especially small in the proximity of the fibres, indicating that the tendency for the fibres to hold the crack shut at is distributed over the whole crack face, rather than local to each fibre. This is in part due to the low interfacial friction typical for the Ti/SCS-6 SiC system, which means that the bridging stress is distributed over a large volume of material and not just near the crack plane.
The COD profiles recorded along the dashed line in figure 5 for the crack increments Fs0, Fs1, Fs2 and Fs7 are shown in figure 6 at and . This line lies solely within the matrix passing by the fibres. Note that in each case the COD fluctuates locally. The large CODs measured for the unloaded cases are worthy of consideration. This has been called the residual CODr by Davidson (1992). In fact, it is much larger than the changes in opening displacement ΔCOD observed on loading to , which are only a few microns, even near the mouth of the crack. There are a number of factors that contribute to CODr; firstly, it should be noted that the composite is ordinarily thermally stressed as a result of manufacture. As we shall see in §4b, the longitudinal fibre thermal residual stresses are typically around −1000 MPa. As has been discussed by Rauchs et al. (2004), when the crack by-passes the fibre, these stresses act to prop open the crack. The second factor is the fact that the bridging fibres tend to pull-out slightly under tension. This means that when the load is removed, the fibres tend to be too long in the crack region. This also acts so as to introduce a compressive stress into the bridging fibres at the crack plane (see figure 11). Both mechanisms thus tend to wedge open the crack at causing a positive stress intensity at the crack-tip (see figure 12) and a significant residual CODr. It is also clear that while the COD varies from point to point, it broadly follows a √r line where r is the distance from the crack-tip in accordance with the analysis of Budiansky & Amaziago (1989).
(b) Crack stress field
Of course, X-ray imaging tells just one side of the story. As the crack grows, the stresses in the matrix and fibres redistribute. In figures 7 and 8, the matrix and fibre strain fields are shown at and , respectively. There are a number of points worthy of mention. It is clear that the stress fields in the matrix and fibres are essentially complementary. In the absence of an applied load, the far-field stresses are likely to be due solely to the thermal residual stresses introduced on cooling from the fabrication temperature (approx. 900°C). As one would expect, the matrix is in residual tension (strain approx. 0.4%) and the fibres under compression (−0.25%). These longitudinal elastic strains are indicative of stresses around 460 and −1000 MPa, respectively (Withers & Clarke 1998), and represent the stresses that would be generated by the elastic accommodation of the thermal expansion misfit strains upon cooling from around 870°C. These stresses are in good agreement with those observed previously (Hung et al. 2009). It is also evident that at the fibres are essentially in axial compression everywhere, although the strain (stress) is least compressive in the wake region of the crack.
Unsurprisingly, at all stages of crack growth, the stress in the matrix is essentially zero at and in the region of the crack. It is also clear that the strain intensity at the crack-tip is relatively indistinct and that the peak strain at the crack-tip decreases somewhat with increasing crack length (increasing numbers of bridging fibres) despite the increasing nominally applied stress intensity. It is also clear that the perturbed region is approximately ‘V-’ (or wedge-)shaped extending around 1 mm on either side of the crack plane, as observed previously (Preuss et al. 2003; Sinclair et al. 2004). It is evident in figure 8 that for the matrix the unloading wedge starts near the crack-tip, but that for the fibres the preferentially loaded wedge extends a little ahead of the crack-tip (see also figure 10b). This is due to the onset of sliding ahead of the crack-tip in the crack-tip stress field. The vertical extent of this wedge-shaped region increases as the crack progresses. The extent of this wedge has been shown in previous work (Hung et al. 2009) to become narrower the higher the interfacial strength. It is also clear that even at the fibres only climb into tension in the region of the crack/crack wake (this is seen even more clearly in figure 11). The tensile strain in the fibres bridging the crack increases only slightly with increasing crack length.
Upon unloading to , the fibre strain along the crack plane becomes slightly compressive as the crack is propped open somewhat and there is limited reverse sliding (figure 8). This leaves a slight tensile peak in the fibre strain around 0.25–0.50 mm from the crack plane because the reverse sliding length is shorter than the forward one.
It is possible to infer the macrostress from a knowledge of the stress in the constituent phases. Assuming that the axial stresses are the only significant stresses, we can write (Withers et al. 1989) 3.1This has been applied to the phase strains to create maps of the macrostress field at and such as those in figure 9 for Fs3. The shape is in broad agreement with expectation and that observed for cracks in monolithic materials (Steuwer et al. 2010; Lopez-Crespo et al. 2012) except that there are significant tensile stresses transferred across the crack faces at . The far-field stresses are in reasonable agreement with those nominally applied (at ; σMacro≈35 MPa and at ; σMacro≈350 MPa). At , just ahead of the crack-tip, the stress is significantly tensile (>150 MPa) indicative of a significant stress intensity at the crack-tip. This corroborates the thesis that there exists a significant bridging-induced crack opening stress arising from the compressive stresses in the bridging fibres propping the crack open as observed in figure 6. This will significantly reduce the range of stress intensity experienced by the crack-tip and increase the actual R ratio, as has been commented by Rauchs et al. (2004) among others. At , the macrostress averaged over the finite gauge volume reaches a value in excess of 500 MPa, which is around twice the far-field value ahead of the crack-tip.
(a) Interfacial stresses
Following previous analyses (Preuss et al. 2002; Hung et al. 2009), the interfacial shear strength can be inferred directly from the gradient in the fibre stress along the fibre direction. The fibre strains recorded at a distance of around 360 μm from the notch (marked by the dashed horizontal line in figure 5) have been differentiated and analysed to show the interfacial stress at at various stages of fatigue crack growth. It is evident that, in agreement with the observations by Hung et al. (2009), the interfacial shear stress is not constant with distance from the crack plane but rises to a peak stress (here around 50–60 MPa compared with 60–80 MPa in their case) at the boundary of the sliding zone. This boundary shifts as the fatigue crack advances from around 0.5 mm from the crack plane after Fs1 to around 1mm after Fs7 (figure 10a). Between these boundaries, the sliding stress falls sharply towards the crack plane predominantly because of increasing wear, but also due to the decreasing radial clamping force from the Poisson contraction in response to the increasing tensile fibre stress near the crack plane. This is contrary to the simplifying assumption used in analytical models that the interfacial shear stress is constant in the sliding region. The effect of interfacial wear occurring during repeated backwards and forwards sliding of the interfaces has been proposed for some time (Mackin et al. 1992). Our findings are in good agreement with Zok and co-workers who measured an average interfacial shear stress after fatigue wear of around 20 MPa (Walls et al. 1993) in this zone and is significantly higher than the value (9 MPa) inferred by John et al. (1998) from COD measurements. Analysis of the curves for different numbers of cycles suggests that the interfacial stress that can be borne by the interface in the sliding region (between the two peak stresses) falls with repeated fatigue cycling as the crack grows. Walls & Zok (1994) proposed a linear increase in frictional sliding stress rising from zero at the notch, which is exactly what is found to be the case here and could be because the region nearest the notch sees the most sliding and is most prone to wear. Extensive wear degradation has been confirmed in this region by post mortem destructive analysis (Hung & Withers 2012).
The peak interfacial shear stresses delineate the extent of the sliding zone plotted in figure 10b. From this figure, it is notable that the sliding length either side of the crack-plane varies linearly with distance behind the crack-tip (figure 9b), with zero sliding length occurring some 300 (Fs1) to 700 μm (Fs7) ahead of the crack-tip.
(b) Fibre bridging stresses
As discussed earlier, the crack bridging stress in the fibres in the vicinity of the crack at and is responsible for shielding the crack-tip from much of the applied driving force by limiting the change in crack opening. In reality, the stress is transferred to the matrix over the whole of the load transfer region shown in figure 7. However from a crack-tip shielding viewpoint, most analyses distribute the bridging stress across the crack faces and a number of models for this have been sketched in figure 1. The actual stresses measured in the fibres at the crack plane (z=0) are shown in figure 11.
A number of important points are evident from figure 11. Firstly, it is clear that the stress in the bridging fibres varies little with distance from the crack-tip increasing only slightly with distance towards the notch and only slightly with increasing crack length. This is in contrast to the forms proposed in figure 1, except for a fairly low gradient version of curve B. Indeed it is in broad agreement with the result obtained by Buchanan et al. (1997) for longer (approx. 7 mm) cracks in Timetal/SCS-6SiC composite. They inferred a B-shaped curve response having a maximum bridging fibre stress difference (between and of around 1200 MPa at the notch and 500 MPa near the crack-tip compared with around 1100 and 800 MPa, respectively, in our case. They found that irrespective of crack length the difference between fibre bridging stress at and at the notch and at crack-tip varied little so that all the bridging stress difference curves fell onto a single line if normalized by the overall crack length. This is also the case here although with a significantly smaller difference between the values at the notch and crack-tip.
The stresses in the bridging fibres are significantly lower than the pristine fibre strength (approx. 5 800 MPa), and are just over half those recorded for non-pristine fibres (approx. 2 000 MPa) (Preuss et al. 2002) so fibre failure might be expected to occur only occasionally. In this case, there appears to be no evidence in the tomographs that any of the undamaged fibres have broken. For all the crack lengths measured, not just those shown here, the fibre stresses oscillate from each lateral measurement location to the next at (illustrated by the dotted lines for the Fs7 response in figure 11); this is probably due to the ‘hexagonal’ arrangement whereby every other measurement location contains on average one more fibre (see figure 6). As noted in the maps of figure 8, it is evident that the bridging fibres at are in compression. The bridging fibres are stressed to approximately −250 MPa, varying little with increasing crack length. The fibre stresses fall to a level close to the thermal stress far beyond the crack-tip for short cracks at Kmin. At , there is a bending component of stress in the remaining uncracked ligament, which becomes significant as the crack length approaches half the original sample width (W). Finally, it should be noted that these thermal stresses that keep the crack open at are commonly ignored in crack-tip shielding analyses.
(c) Crack-tip shielding evaluated from the fibre bridging stresses
It is possible from a knowledge of the stresses in the fibres bridging the crack (figure 11) to calculate the crack closing tendency expressed in terms of a crack-tip shielding stress intensity, Kshield. To do this, we can smear the fibre bridging stresses over the crack plane to determine Δσbridge as a function of distance from the notch. From this, we can calculate the contribution to the stress intensity range from crack bridging using a weight function method: 4.1where h(x,a) is the weight function. In the present case, we have used the solution by Wu (1984) and the results are plotted in figure 12 from which it is clear that the shielding has a negative stress intensity at . This is of course because the thermal stresses hold the crack open. This acts to reduce the range of stress intensity experienced by the crack-tip. In a case similar to the current one, Rauchs et al. (2004) predicted a stress intensity contribution initially rising quickly with the number of bridging fibres before stabilizing at −5 or −7 MPa√m for 10 bridging fibres with Coulomb friction coefficients, μ, of 0.2 and 0.1, respectively. Our experimental measurements of frictional sliding stress, approximately 50 MPa in the fatigued zone, suggest an effective Coulomb friction coefficient around 0.13 so that the two cases are quite comparable. The agreement between our measurements in figure 12 at with the above values is reassuringly good.
It is also clear from figure 12 that at the crack-tip shielding increases approximately in line with the nominally applied stress being about 50 per cent of . Consequently, the effective stress intensity range, ΔKeff, increases only slowly with increasing crack length despite the sharp rise in ΔKAppl. Another point worthy of note (see table 2) is that the effective R ratio experienced at the crack-tip is much larger than the 0.1 nominally applied. This has been remarked upon previously, though our rise is somewhat lower than that predicted by FE (Rauchs & Withers 2002), i.e. around Reff=0.85 for 3–5 bridging fibres.
(d) Crack-tip shielding evaluated from the crack opening displacements
Following the work of Budiansky & Amaziago (1989), it is possible to infer the crack-tip shielding directly from the COD. They predicted that the COD would vary as √r, where r is the distance from the crack-tip, arriving at the relation: 4.2where Ec is the composite stiffness, νm the matrix Poisson's ratio, M the gradient in a linear plot of COD versus √r, and A an orthotropic factor (Budiansky & Amaziago 1989) (here approx. 1.6). The crack-tip opening displacements at and are shown in figure 6. It can be seen that while there is considerable point to point variation in the COD with position, the overall curves are reasonably consistent with a √r relation. Following this approach, the crack-tip stress intensity range experienced by the crack-tip, ΔKeff can be inferred from curves such as those in figure 6. The results are summarized in table 2 and are plotted in figure 13. It is worth noting that while the effective stress intensity ranges determined from ΔCOD values are in relatively good agreement with the level of crack-tip shielding derived from the crack bridging, the COD at is much bigger than one would expect in terms of . Presumably, this is because of the complex hysteretic response of the fibre sliding and local plasticity taking place in the crack zone that the simple COD model cannot replicate. Certainly, finite element modelling of incremental crack growth also predicts large COD values (Hung 2009).
(e) Crack-tip shielding evaluated from the crack-tip stress field
The matrix crack-tip stress field was compared with the linear elastic fracture mechanics prediction based on Westergaard's solution (Westergaard 1939; Ewalds & Wanhill 1984). The stress in the crack opening direction, σy, is described as 4.3where KI is the opening mode stress intensity factor and (r, θ) are the polar coordinates, with the origin at the crack-tip. Because the region behind the crack-tip differs substantially between monolithic and fibre composites, only data from the region ahead of the crack-tip were used in the fitting. Both the loaded and unloaded fields were fitted and the inferred stress intensity range is shown in figure 13 and summarized in table 2. Despite some scatter, it is clear that in accordance with the other two measures of the driving force, the crack-tip stress intensity remains at around 10 MPa√m as the crack grows while the nominally applied stress intensity must be ramped up in order to maintain growth of the crack.
To the authors' knowledge, this experiment is the first to combine X-ray imaging and X-ray tomography to derive a range of fracture mechanics parameters. The effective stress intensity has been derived in three complementary ways; by measurement of the COD, by measurement of the bridging forces acting on the crack and by comparing the crack-tip stress field with linear elastic predictions. This approach can potentially be applied widely, allowing the damage mechanism occurring ahead of the crack and the shielding arising behind the crack to be quantitatively assessed (Withers 2011) in many cases where the microstructure acts to shield the crack-tip. In the present case, the tomography and diffraction modes have enabled the following conclusions to be drawn.
The tomography has shown that the crack tends to bifurcate as it by-passes fibres such that the crack is not planar nor does it propagate particularly evenly. It has revealed a crack that is held open at owing to a combination of compressive thermal residual stresses in the fibres and the slight pull-out of the fibres that occurred at both of which act to maintain a significant crack-tip stress field at . Despite the very significant stress intensities applied, especially when the crack is long, the crack opens only by a further few microns at indicative of high levels of crack-tip shielding. The change in COD has been used to evaluate the crack-tip stress intensity, which has been found in this case to lie in the region of 10 MPa√m throughout crack growth.
The diffraction has shown that significant compressive stresses (approx. −250 MPa) arise in the bridging fibres at which helps us to explain why the significant crack opening is observed at . This is some 750 MPa less compressive than in the fibres far from the crack. Even at only in a relatively small region bridging the crack and ahead of the crack is the fibre stress significantly tensile. The distribution of fibre bridging stresses is similar to that predicted by Danchaivijit & Shetty (1993) and Chiang et al. (1993) in figure 1 (curve B); though further work remains to critically compare the predictions and underlying assumptions of such models in the light of the new evidence of the fictional sliding strength, the sliding lengths and the fibre bridging stresses are presented here. In accordance with the inferences made by Buchanan et al. (1997), the fibre bridging stress at the notch (900 MPa) and at the crack-tip (approx. 600 MPa) at varies little with crack growth. Consequently, the increase in crack-tip shielding as increasing numbers of fibres are by-passed is more to do with the increase in the number of bridging fibres rather than an increase in the stress the fibres bear. A simple approximation would be to say that all the fibres bridging the crack are stressed to around 750 MPa. The tensile stresses were well below those normally needed to fracture the fibres. Indeed, no fibre fracture was observed except for fibres damaged by the electrodischarge machining process used to prepare the sample. The bridging stresses have been used to determine the effective crack-tip stress intensity at , which due to their shielding effect, is only about a half of the nominal stress intensity. At , the compressive stresses in the bridging fibres hold the crack open, maintaining a significant tensile stress at the crack-tip (approx. 150 MPa). This negative crack-tip shielding at plays a major role in reducing the range of stress intensity experienced over the fatigue cycle. The effective stress intensity range determined in this way was of order 10 MPa√m even when the applied stress intensity range had increased to 60 MPa√m.
The negative crack-tip shielding at arising from the combined effect of the relaxation of the compressive fibre thermal stresses and the tendency for the fibres to be pulled out from the matrix in the crack-tip region at significantly reduces both the stress intensity range and the R ratio. This negative stress intensity at is in good agreement with the level (approx. −5 to −7 MPa√m) predicted by finite element modelling (Rauchs & Withers 2002). The stresses in the fibres and matrix were combined to determine the macrostress distribution. The stress intensity was also determined by comparing the matrix stress field ahead of the crack to that expected by linear elastic fracture mechanics. Again effective stress intensities of around 10 MPa√m were obtained irrespective of crack length. This is a key result demonstrating that a Paris type of fatigue crack growth law is not appropriate for such materials. This is in accordance with work by Bowen et al. (Cardona et al. 1993; Cotterill & Bowen 1993), who demonstrated non-Paris law behaviour for Ti-SiC composites with increasing numbers of bridging fibres with increasing crack growth. Indeed their experimental work shows crack growth until ultimate arrest at ΔKApp=10 MPa√m for Ti-6Al-4V/Sigma SiC fibre composite. Akiniwa et al. (2007) found fatigue threshold values below 10 MPa√m for Ti-15-3/SCS-6 SiC composites.
It is reassuring that the three methods for evaluating the crack-tip stress intensity range deliver similar conclusions; however, there are still outstanding questions. It should be noted that the and values are both significantly greater than conventional models would predict. This is probably because models tend to neglect hysteretic sliding effect and represent the interfacial stress in a rather simplistic way. The current work indicates that the interfacial sliding stress varies both along the fibres and with distance from the crack-tip. This is almost certainly a consequence of interfacial wear occurring during repeated backwards and forwards sliding of the interfaces. Indeed, the interfacial stresses transmitted across the fibre interface near the crack plane are negligibly small in stark contrast to simple constant interface friction models. This finding is in good agreement with earlier work that identified interfacial wear as an important issue (Mackin et al. 1992). Zok and co-workers measured an average interfacial shear stress after fatigue wear of around 20 MPa (Walls et al. 1993) and subsequently proposed a linear increase in frictional sliding stress rising from zero at the notch (Walls & Zok 1994), which is exactly that found to be the case here. Similar effects have also been observed for the same composite at elevated temperature (Hung & Withers 2012).
It is also worth remembering that most analytical models, as well as having very simplistic interfacial sliding criteria, assume planar cracks of equal length all along the front. The tomography shows that this not to be the case here nor is it probably in general. As a result, while this muddies the interpretation of the diffraction results because the beam samples the stress field through the whole thickness of the sample, it does provide a realistic picture of the smeared nature of the crack-tip stress field when considered over engineering dimensions and hence a more realistic picture of the driving force for crack growth at the crack-tip. While Ti/SiC composites provide a classic example where imaging and tomography enable a multi-facetted picture of the fatigue crack process to be established, we believe that the combined diffraction and imaging approach, we have termed crack-tip microscopy analogous to the modes used in electron microscopy on thin samples, will enable a better understanding of the cracking of many complex microstructured materials from transformation toughened ceramics to self-healing materials.
The authors are grateful to Tim Doel and Prof. Paul Bowen at Birmingham University for precracking the Ti/SiC samples and to Dr Matthew Peel and Marco di Michiel the ID15 ESRF beamline staff. PJW acknowledges helpful discussions with Prof. James Marrow. Funding is acknowledged through EPSRC grants EP/F007906, EP/F028431 and EP/I02249X.
- Received February 7, 2012.
- Accepted March 27, 2012.
- This journal is © 2012 The Royal Society